I was confused by what it means when a Random variable is a deterministic function of another Random variable yet is independent of it? How is this possible?

Here's the question: Consider three random variables $X,Y$ and $Z$ such that $Z$ is independent of $X$ and of $Y$ and is a deterministic function of $(X,Y)$. Is $H(Z)=0$? If so prove it; if not, give a counter example.